Generator of translation for the hyperbolic plane? - MathOverflow [closed] most recent 30 from http://mathoverflow.net 2013-05-22T02:07:49Z http://mathoverflow.net/feeds/question/66709 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/66709/generator-of-translation-for-the-hyperbolic-plane Generator of translation for the hyperbolic plane? Mike Stay 2011-06-02T05:30:11Z 2011-06-02T06:05:34Z <p>What is the generator of translation in the Beltrami-Klein model of the hyperbolic plane?</p> http://mathoverflow.net/questions/66709/generator-of-translation-for-the-hyperbolic-plane/66710#66710 Answer by robot for Generator of translation for the hyperbolic plane? robot 2011-06-02T06:05:34Z 2011-06-02T06:05:34Z <p>Hyperbolic plane is a homogeneous space $G/H$ where $G$ acts by isometries and so any reasonable defined `translation' is given by the natural left action of $G$. Decide what elements of $G$ will you call translations and then for any abstract generator $X\in\mathfrak{g}$ such that $\exp{tX}$ is translation, compose the natural left action with diffeomorphism of $G/H$ to your favorite model. Differentiate the resulting map at zero and you are done.</p> <p>If I am not mistaken, this question is more suitable for math.SE.</p>